Question: Simplify. Rewrite the expression in the form $4^n$. $4^4\cdot 4^3=$
$\begin{aligned} 4^4\cdot 4^3&=4^{4+3} \\\\ &=4^{7} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 4^4\cdot 4^3&=\underbrace{4\cdot 4\cdot 4\cdot 4}_\text{4 times}\cdot\underbrace{4\cdot 4\cdot 4}_\text{3 times} \\\\\\ &=\underbrace{4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4}_\text{7 times} \\\\ &=4^{7} \end{aligned}$ In conclusion, $4^4\cdot 4^3=4^{7}$.